10. Thin Lizzy

Fronted by Phil Lynott, these rockers had their biggest chart success with "The Boys Are Back in Town," which went to No. 12 on the Hot 100 in 1976.

9. The Irish Rovers

The Irish Rovers hit No. 7 in 1968 with their hit "The Unicorn."

8. The Cranberries

Perhaps best known for their hit "Zombie," the group, led by Dolores O'Riordan, climbed to No. 8 on the Hot 100 with "Linger" in 1994.

7. The Script

The Script ascended to No. 12 on the Hot 100 in 2010 with this song, though it was written in 2008.

6. Enya

While she's probably better known for "Orinoco Flow" or "Sail Away," Enya's biggest chart success actually came from her involvement with this tune (it samples the Fugees's "Ready Or Not," which was itself based on a slowed-down sample of Enya's 1987 tune "Boadicea"). The song went to No. 2 in 2004.

5. Snow Patrol

Placement in Grey's Anatomy helped this song hit No. 5 on the Hot 100 in 2006.

4. Van Morrison

Van the Man's highest-charting hit isn't "Moondance" or "Brown-Eyed Girl;" it's this up-tempo raver from 1970's His Band and the Street Choir, which climbed to No. 9 on the Hot 100 in 1971.

3. Sinéad O'Connor

This massive, Prince-penned hit climbed to No. 1 in 1990 and stayed there for four weeks, aided by O'Connor's performance in the minimalistic, marvelously emotive video.